Yes, but the majority of the funding goes to the increasingly bloated institutional overhead. NYU takes 61% of research grants [1], while Columbia takes 64.5% [2]. That doesn't include other fees that PIs might pay in addition. These percentages keep going up year-over-year and are even into the 70% range at some institutions.

[1]: https://www.nyu.edu/content/dam/nyu/research/documents/OSP/N... [2]: https://www.finance.columbia.edu/sites/default/files/content...